Dynamic analysis of shallow shells of rectangular base

In this investigation a systematic analytic procedure for the dynamic analy sis and response of thin shallow shells with a rectangular layout is presen ted. The shell types examined are the elliptic and hyperbolic paraboloid, t he hypar, the conoidal parabolic and the soap-bubble shell, although in pri nciple any shell geometry expressed by a continuous surface equation can be treated. The eigenvalue problem solution is based on the one hand on the c onsideration of the shell as a system of two interdependant plates whose bo undary conditions comply with the prevailing bending and membrane boundary conditions of the shell, and on the other hand on the consistent use of bea m eigenfunctions, in the context of a Galerkin solution procedure. The seri es solution obtained in this way converges rapidly and provides practically acceptable results even in cases with one or more free edges, where the bo undary conditions cannot be strictly satisfied. The whole analysis is carri ed out on the basis of a few non-dimensionalized geometrical parameters, wh ich are the only input required for the computer program specially written for that purpose. (C) 1998 Academic Press.